CUET Mathematics 2023 22 May Shift 3 PYQs

If objective function $Z = 20x + 30y$ of an LPP is subject to the constraints $3x + 4y \geq 12$, $4x + y \geq 4$, $x \geq 0, y \geq 0$, then Z has :

(A) Min at (0, 4)

(B) Max at (0, 4)

(C) Min at (4, 0)

(D) Max at (4, 0)

(E) Min at $\left(\frac{4}{13}, \frac{36}{13}\right)$

Choose the correct answer from the options given below :

The corner points of feasible region determined by the following system of linear inequalities $2x + y \leq 10, x + 3y \leq 15, x \geq 0, y \geq 0$ are $(0,0), (5,0), (3,4)$ and $(0,5)$, then the relation between p and Q so that minimum of Z occurs both points $(3,4)$ and $(0,5)$ is :

The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$, are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is :